Addendum: Hubble Space Telescope Evidence for an Intermediate-Mass Black Hole in the Globular Cluster M15. II. Kinematic Analysis and Dynamical Modeling [Astron. J. 124, 3270 (2002)]

In Paper II, we reported the existence of a dark and compact mass component near the center of M15, based on an analysis of new data from the Hubble Space Telescope. Possible explanations for this mass component include (1) a single, intermediate-mass black hole (BH) and (2) a collection of dark remnants (e.g., neutron stars) that have sunk to the cluster center because of mass segregation. We assessed the plausibility of the latter possibility by comparing the kinematic data for M15 with the predictions of the most sophisticated and most recently published Fokker-Planck models for M15 (Dull et al. 1997, hereafter D97). We showed that the mass-to-light ratio (M/L) profile in Astron. J. 124, 3270 (2002) implies too few dark remnants near the cluster center to explain the observed kinematics of M15. This supported the view that M15 harbors an intermediate-mass BH. We address here how this conclusion is affected by the recent discovery of an error in Figure 12 of D97. We show that the presence of an intermediate-mass BH continues to be a viable interpretation of the data, but that its presence ceases to be uniquely implied. After we completed Paper II, Dull et al. discovered an unfortunate error in their Figures Astron. J. 124, 3270 (2002) and Astron. J. 124, 3270 (2002). The labeling along the horizontal axes of these figures is incorrect as the result of a coding error in Astron. J. 124, 3270 (2002) plotting routines (H. Cohn & B. Murphy 2002, private communication). The units along the top axis should have read ``arcmin'' instead of ``pc,'' and the labeling in arcminutes along the bottom axis is incorrect. The net result is that the radial scale of these figures is too compressed by a factor of 2.82. The true total mass of the centrally concentrated population of dark remnants in the Fokker-Planck models is therefore considerably larger than what was implied by the M/L profile shown in Figure 12 of D97. Figure 1 shown here is similar to Astron. J. 124, 3270 (2002), but it now shows the data-model comparison with the corrected D97 M/L profile. Models without a BH are now found to be statistically acceptable (within 1 σ), although inclusion of an intermediate-mass BH, with M_BH=1.7^+2.7_-1.7×10³ M_solar, still provides a marginally better fit to the data (although not a statistically significant one). Hence, the Fokker-Planck models for M15 discussed by D97 do in fact have enough dark remnants near the cluster center to explain the observed kinematics. However, the D97 models still have a number of important shortcomings, as discussed in Astron. J. 124, 3270 (2002). Most importantly, D97 assumed that all neutron stars that form in the cluster are retained. By contrast, the observed distribution of pulsar kick velocities indicates that the retention factor should only be a few percent; most authors agree that it should be no more than 10% (see references in § 5.4 of Paper II). In this sense, the D97 models provide an upper limit on the number and mass of dark remnants in M15. The same is true for the N-body models constructed recently by Baumgardt et al. (2002), the results of which are qualitatively similar to those of D97. More realistic evolutionary models that include neutron star escape will require a more massive and more statistically significant BH to fit the data than that suggested by Figure 1. Alternatively, one can assume that there are more stars in the high-mass end of the initial mass function, or that the transition between stars that evolve to white dwarfs as compared with neutron stars occurs at a higher initial mass (H. Cohn & B. Murphy 2002, private communication). Independent evidence does not exist to support these assumptions, although they cannot be ruled out. The evidence for a central BH in M15 is less convincing than it was on the basis of our earlier analyses. However, because of the somewhat unrealistic assumptions about neutron star retention in the models of D97 and Baumgardt et al. (2002), and because of the independent evidence for a BH in another cluster (G1; Gebhardt, Rich, & Ho 2002), the presence of a BH in M15 continues to be a viable interpretation of the data. The best-fit BH mass with the corrected D97 M/L profile is M_BH=1.7^+2.7_-1.7×10³ M_solar (see Fig. 1); with a constant M/L, it is M_BH=(3.2+/-2.2)×10³ M_solar (see § 5.4 of Paper II). A model that includes both neutron star escape and mass segregation would probably yield a value between these numbers. So if M15 has a BH, its mass is consistent with the correlation between velocity dispersion and BH mass that has been inferred for galaxies (see Astron. J. 124, 3270 (2002)). This continues to suggest the possible existence of an important new link between the structure, evolution, and formation of globular clusters, galaxies, and their central BHs (see Astron. J. 124, 3270 (2002) and also Gebhardt et al. 2002). However, with the presently available models and data it is neither uniquely implied nor ruled out that M15 has an intermediate-mass BH. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with proposal 8262.